Climate system is a complex system， which can exist in dual （alternative /multiple） stable states. When the control parameters of the system are near the critical point， the small change of the control parameters or the small interference from the outside may lead to the irreversibly abrupt change of the system state from one stable state to another stable state， which is called the critical transition. This review systematically summarizes the basic theory and main research contents of critical transition in climate system， discusses its research trend， and puts forward existing problems and key research directions. The results show that： \mathrm{①} The current research mainly focuses on the phenomenon of critical transition in subsystem of climate system at different spatio-temporal scales and corresponding research methods， the driving factors and formation mechanism of critical transition， and the early warning signals and detection methods of critical transition. \mathrm{②} The research of critical transition in climate system tends to expand the research scale and scope and to carry out interdisciplinary research. It also emphasizes the cascading effect and tends to carry out global integrated research. In addition， related researches are seeking positive coping strategies to prevent the negative effects of critical transition. \mathrm{③} The problems of existing research include： the cognition and use of basic concepts need to be unified and standardized， data accessibility and accuracy of quantitative analysis model need to be improved， and critical transition and its potential climate risks need to be further studied. \mathrm{④} Future research in China should focus on the relationship between critical transition and China's key ecological security barriers （e.g.， the Tibetan Plateau）， regional development patterns， and human security and well-being. Based on the bifurcation theory of climate dynamics system and the research progress of critical transition in climate system， this review can provide reference for the study of climate change and earth system in China.